There are in essence only two choices, go before or go after. If the go before fails that is the equivalent to go after. Conversely, if the go after fails, then that is equivalent to go before.
So, in event that H is not after F, the condition H before G fails. Since it failed, H must go after G or said conversely, G must go before H. Thus G-H-F.
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So, in event that H is not after F, the condition H before G fails. Since it failed, H must go after G or said conversely, G must go before H. Thus G-H-F.
So when H-G triggers, then it must also be true that F-H triggers. So we have F-H and H-G, which means F-H-G.
But what about the contrapositive? The CP of a biconditional is just the negation of both sides. So,
/H-G<--->/F-H
But what does it mean if H is not before G? That G is before H!
So, G-H
And what does it mean that F is not before H? That H is before F!
H-F
Combining these two we have:
G-H-F.
Hope this helps!